if we have a square and its length is half of the breadth and breadth equals to x and th perimeter is 128 what will be the length??
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Answer:
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Step-by-step explanation:
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Page No 222:
Question 1:
Find the perimeter of a rectangle in which:
(i) length = 16.8 cm and breadth = 6.2 cm
(ii) length = 2 m 25 cm and breadth = 1 m 50 cm
(iii) length = 8 m 5 dm and breadth = 6 m 8 dm
ANSWER:
We know: Perimeter of a rectangle = 2×(Length+Breadth)
(i) Length = 16.8 cm
Breadth = 6.2 cm
Perimeter = 2×(Length+Breadth)
= 2×(16.8+6.2) =46 cm
(ii) Length = 2 m 25 cm
=(200+25) cm (1 m = 100 cm )
= 225 cm
Breadth =1 m 50 cm
= (100+50) cm (1 m = 100 cm )
= 150 cm
Perimeter = 2×(Length+Breadth)
= 2×(225+150) =750 cm
(iii) Length = 8 m 5 dm
= (80+5) dm (1 m = 10 dm )
= 85 dm
Breadth = 6 m 8 dm
= (60+8) dm (1 m = 10 dm )
= 68 dm
Perimeter = 2×(Length+Breadth)
= 2×(85+68) =306 dm
Page No 222:
Question 2:
Find the cost of fencing a rectangular field 62 m long and 33 m wide at Rs 16 per metre.
ANSWER:
Length of the field = 62 m
Breadth of the field = 33 m
Perimeter of the field = 2(l + b) units
= 2(62 + 33) m =190 m
Cost of fencing per metre = Rs 16
Total cost of fencing = Rs (16×190) = Rs 3040
Page No 222:
Question 3:
The length and the breadth of a rectangular field are in the ratio 5 : 3. If its perimeter is 128 m, find the dimensions of the field.
ANSWER:
Let the length of the rectangle be 5x m.
Breadth of the rectangle = 3x m
Perimeter of the rectangle = 2(l + b)
= 2(5x + 3x) m
= (16x) m
It is given that the perimeter of the field is 128 m.
∴16x=128⇒x=
128
16
=8∴Length =(5×8
Step-by-step explanation:
Page No 222:
Question 6:
Find the perimeter of a square, each of whose sides measures:
(i) 3.8 cm
(ii) 4.6 cm
(iii) 2 m 5 dm
ANSWER:
(i) Side of the square = 3.8 cm
Perimeter of the square = (4×side)
= (4×3.8) = 15.2 cm
(ii) Side of the square = 4.6 cm
Perimeter of the square = (4×side)
= (4×4.6) = 18.4 cm
(iii) Side of the square = 2 m 5 dm
= (20+5) dm (1 m = 10 dm)
= 25 dm
Perimeter of the square = (4×side)
= (4×25) = 100 dm
Page No 222:
Question 7:
The cost of putting a fence around a square field at Rs 35 per metre is Rs 4480. Find the length of each side of the field.
ANSWER:
Total cost of fencing = Rs 4480
Rate of fencing = Rs 35/m
Perimeter of the field =
Total cost
Rate
=
Rs 4480
Rs 35/m
=
4480
35
m=128 m
Let the length of each side of the field be x metres.
Perimeter = (4x) metres
∴4x=128⇒x=
128
4
=32
Hence, the length of each side of the field is 32 m.
Page No 222:
Question 8:
Each side of a square field measures 21 m. Adjacent to this field, there is a rectangular field having its sides in the ratio 4 : 3. If the perimeters of both the fields are equal, find the dimensions of the rectangular field.
ANSWER:
Side of the square field = 21m
Perimeter of the square field = (4×21) m
= 84 m
Let the length and the breadth of the rectangular field be 4x and 3x, respectively.
Perimeter of the rectangular field = 2(4x + 3x) = 14x
Perimeter of the rectangular field = Perimeter of the square field
∴14x=84 ⇒x=
84
14
=6
∴ Length of the rectangular field =(4 × 6) m=24 mBreadth of the rectangular field = (3 × 6) m=18 m